Theme Essential Question: How does mathematical reasoning apply to the attributes of two- and three- dimensional figures as seen in everyday life?
Essential Questions:
What can you conclude about the measures of angles of a triangle?
Standards
8.G.5.Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Note: This standard has been divided into three lessons to allow for ample time for students to obtain fluency.
Objectives
The student will use the sum of the interior angle measures in a triangle to calculate missing angle measurements.
The student will use an informal argument to explain the sum of the interior angle measurement is 180°.
The student will develop an informal argument and use their argument to apply the relationship between the exterior angle of a triangle with their corresponding remote interior angles.
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team Students should continue to approach this lesson as indicated in the discussion for lesson 2-4.
By using three copies of the same triangle labeled and placed so that the three different angles form a straight line, students can: explore the relationships of the angles, learn the types of angles (interior, exterior, alternate interior, alternate exterior, corresponding, same side interior, same side exterior), and Explore the parallel lines, triangles and parallelograms formed.
Angles.png
Assessment Product
Students should continue reviewing the problem solving connections on page 137-140 in the OnCore book. The final presentation of the “Where in the park is Xander?” can be presented as a PowerPoint, poster, etc. This will conclude the end of this unit.
Students can also take “Where in the park is Xander?” and extend and/or recreate a new scenario.
Key Questions
Why does the sum of the interior angles of a triangle equal 180°?
Why does an exterior angle of a triangle equal the sum of the remote interior angles?
How do you apply the sum of the interior angles of a triangle equal 180°?
How do you apply that an exterior angles of a triangles equal the sum of the remote interior angles
Observable Student Behaviors
The student can provide a viable argument to justify the facts about the angle sum and exterior angles of triangles.
The student can determine the measurement of the interior and exterior angles of triangles.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Suggested Activities [see Legend to highlight MCO and HYS]
On Core Mathematics Unit 5-2, p. 117-120
ABC Mastering the Common Core in Mathematics Chapter 11-1 through 11-2, p. 167-169
Gizmo Lessons
Investigating Angle Theorems-Activity A
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
Polygon Angle Sum-Activity B
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. (Student Exploration Sheet & Teacher Guide Available)
Similar Polygons
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity.
Triangle Angle Sum-Activity A
Measure the angles of a triangle and find the sum. Then reshape and resize the triangle and confirm that the sum of angle measures is the same for all triangles.
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
8.G.5- Activity 1(interior) p. 220, Activity 2 (exterior) p. 221
JBHM-7th GP3 (p. 281-314)
Glencoe Geometry Angles of Triangles (Angle Sum Theorem) 4-2 (p.185)
Glencoe Geometry Angles of Triangles (Exterior Angle Theorem) 4-2 (p.186)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Diverse Learners
Odyssey (teacher discretion)
Skills Tutor (teacher discretion)
Math’scool: Unit B Module 8
Homework
See appropriate Glencoe, OnCore, JBHM, and ABC materials
Grade: 8 Unit: 2 Week: 5 Dates: 10/29-11/2
Content: Triangle Angle Theorems
Theme Essential Question:
How does mathematical reasoning apply to the attributes of two- and three- dimensional figures as seen in everyday life?
Essential Questions:
Standards
Note: This standard has been divided into three lessons to allow for ample time for students to obtain fluency.
Objectives
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team
Students should continue to approach this lesson as indicated in the discussion for lesson 2-4.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
http://www.azed.gov/wp-content/uploads/PDF/MathGr8.pdf
(Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 )
By using three copies of the same triangle labeled and placed so that the three different angles form a straight line, students can:
explore the relationships of the angles,
learn the types of angles (interior, exterior, alternate interior, alternate exterior, corresponding, same side interior, same side exterior), and
Explore the parallel lines, triangles and parallelograms formed.
Assessment
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Interior angles, Exterior angles, Remote interior angles
Suggested Activities [see Legend to highlight MCO and HYS]
- On Core Mathematics Unit 5-2, p. 117-120
- ABC Mastering the Common Core in Mathematics Chapter 11-1 through 11-2, p. 167-169
Gizmo Lessons- Investigating Angle Theorems-Activity A
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.- Polygon Angle Sum-Activity B
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. (Student Exploration Sheet & Teacher Guide Available)- Similar Polygons
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity.- Triangle Angle Sum-Activity A
Measure the angles of a triangle and find the sum. Then reshape and resize the triangle and confirm that the sum of angle measures is the same for all triangles.- Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
- 8.G.5- Activity 1(interior) p. 220, Activity 2 (exterior) p. 221
- JBHM-7th GP3 (p. 281-314)
- Glencoe Geometry Angles of Triangles (Angle Sum Theorem) 4-2 (p.185)
- Glencoe Geometry Angles of Triangles (Exterior Angle Theorem) 4-2 (p.186)
Highly Recommended:The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Diverse Learners
Homework
Terminology for Teachers
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http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htmArt, Music, and Media
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